The graph below shows a system of equations: part a: write the equation of each line in slope-intercept form. line p: line q: part b: what is the solution to the system?

Slope-intercept form is:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

You can find the slope either by using the slope formula and finding 2 points:

Or you can use this:

Rise is the number of units you go up(+) or down(-)

Run is the number of units you go to the right

(I'm using rise/run) If you look at line P, from each point you go up 1 unit, and to the right 2 units. So your slope is 1/2. When x = 0, the y value is 6, so your y-intercept is 6.

Line P:

If you look at line Q, from each point you go down 4 units, and to the right 1 unit. So your slope is -4/1 or -4. When x = 0, the y value is -3, so your y-intercept is -3.

Line Q:

To find the solution to the system, you can find the point of intersection(the point where the lines meet). The point of intersection is (-2,5)

You can also do this by hand and set the equation of Line P and Q equal to each other to find x:

Line P: y = 1/2x + 6

Line Q: y = -4x - 3

1/2x + 6 = -4x - 3  Subtract 6 on both sides

1/2x = -4x - 9     Add 4x on both sides

1/2x + 4x = -9   Make the denominators the same

1/2x + 8/2x = -9

9/2x = -9     Multiply 2/9 on both sides to get x by itself

x = -2

Plug in -2 for x into either the equation of Line P or Line Q

y = -4x - 3

y = -4(-2) - 3

y = 8 - 3

y = 5

(-2,5)

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?